Solving Equations

[sail0r]

After working through about 20 of these I have two questions remaining that I just can not find the solution for.

Solve each equation for x, 0?x?2?
(2cosx+?3)sinx=0

&

Solve for x to the nearest hundredth of a radian, 0?x?2?
12sin[sup:2zzo38hj]2[/sup:2zzo38hj]x + sinx-6=0

 

[Deleted member 4993]

After working through about 20 of these I have two questions remaining that I just can not find the solution for.

Solve each equation for x, 0?x?2?
(2cosx+?3)sinx=0
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One set of solutions is

\(\displaystyle \sin(x) \, = \, 0 \, \rightarrow \, x = 0, \, \pi , \, 2\pi\)

and for the other set:

\(\displaystyle \cos(x) \, = -\frac{\sqrt{3}}{2}\)

and continue..
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&

Solve for x to the nearest hundredth of a radian, 0?x?2?
12sin[sup:bgn269b7]2[/sup:bgn269b7]x + sinx-6=0

Use quadratic equation

Please show us your work, indicating exactly where you are stuck, so that we know where to begin to help you

 

[galactus]

Solve for x to the nearest hundredth of a radian, 0?x?2?
12sin[sup:u60dpnzv]2[/sup:u60dpnzv]x + sinx-6=0

Notice this is a quadratic. Let \(\displaystyle u=sin(x)\) and get:

\(\displaystyle 12u^{2}+u-6=0\)

 

[fasteddie65]

Solve each equation for x, 0?x?2?
(2 cos x + ?3) sin x = 0
2 cos x + ?3 = 0 or sin x = 0
2 cos x = - ?3 x = 0, ?, 2?
cos x = -?3/2
x = 5?/6, 7?/6


&

Solve for x to the nearest hundredth of a radian, 0?x?2?
12 sin^2 x + sin x - 6 = 0
12u^2 + u - 6 = 0
What factors of -72 [12 • (-6)] have a sum of 1?
-8 and 9
12u^2 - 8u + 9u - 6 = 0
(12u^2 - 8u) + (9u - 6) = 0
4u(3u - 2) + 3(3u - 2) = 0
(3u - 2)(4u + 3) = 0
3 sin x - 2 = 0 or 4 sin x + 3 = 0
3 sin x = 2 4 sin x = -3
sin x = 2/3 sin x = -3/4

Calculator time!

 

[Deleted member 4993]

Solve each equation for x, 0?x?2?
(2 cos x + ?3) sin x = 0
2 cos x + ?3 = 0 or sin x = 0
2 cos x = - ?3 x = 0, ?, 2? <<< sailor - better be careful copying this part - fast finger eddy had problem here.
cos x = -?3/2
x = 5?/6, 7?/6